1. Evaluate Statistically Based Reports ( AS 3.12) Dru Rose (Westlake Girls High School, Ministry of Education Study Award ) Workshop 1 Margin of Error and Testing Claims in the Media

2. What does AS 3.12 cover? i. Polls and Surveys Non-sampling errors and survey concerns (Workshop 2) Sampling error :Workshop 1 margin of error, 95% confidence intervals for proportions, “rules of thumb”, testing claims ii. Experimental and Observational Studies (Workshop 2) Dru Rose

3. The purpose of this workshop To demonstrate the power of technology for developing the concept of margin of error (making the topic accessible to a wider diversity of students than a theoretical approach relying on the central limit theorem and the normal distribution). To give you a snap-shot of the teaching approach I developed and trialled with a small group of students. Dru Rose

4. Resource Pack Contents (available from www.censusatschool.org.nz after today) www.censusatschool.org.nz 1. The 6 to 7 lesson teaching sequence for sampling error, with teaching notes 2. Power-point slides (sampling error, political polls) 3. 6 media reports 4. Students worksheets and resource materials linked to the teaching sequence 5. 3 csv data files to import into iNZight Dru Rose

5. C1, L2, S5 Margin of error Media Reports have a dual role: They provide a purpose for developing the concepts They provide a real life-context with claims to be tested after developing the concepts Dru Rose

6. C1, L2, S6 Dru Rose

7. C1, L2, S7 Dru Rose

8. C1, L2, S8 Conceptualising a Margin of Error Margin of error involves the sampling variability of a proportion (%) –a categorical parameter Before using a computer simulation, do a concrete activity which mimics what will later be seen in the software Dru Rose

9. C1, L2, S9 Dru Rose

10. C1, L2, S10 I wonder what percentage of all 600 Kare Kare College students travel to school by car? (“motor” on the cards) Sample n = 25 Population 600 students Dru Rose

11. C1, L2, S11 For small sample sizes (n=30), sample proportions (categorical data) are much more variable than sample means or medians (quantitative data) See Wild’s animations Dru Rose

12. C1, L2, S12 Like looking through a window with ripples in the glass “What I see … is not quite the way it really is” Looking at the world using data is

13. C1, L2, S13 Although imperfect, each sample should give a reasonable picture of the population as a whole. In the real world, we usually only have one sample. We want to use this sample to estimate the population parameter. (make an inference) e.g. estimate the percentage of students at Kare Kare College who travel to school by car. Since the sample is representative of the population, we will re-sample from the sample (with replacement) to estimate the sample-to-sample variability ie sampling error or margin of error. Re-sampling from the sample is called Bootstrapping

14. C1, L2, S14 n=100 CI half as long MoE ≈ 10%

15. C1, L2, S15

16. C1, L2, S16 “Opinion Divided on NZ-US exercises” Margin of error % who support resumption 95% CI: Meaning: Judgement: 47.6% 51.3% 43.9% = 47.6% With 95% confidence, we can infer that the % of Nzers who support the resumption of exercises is somewhere between 43.9% and 51.3% Claim of 50% support for resumption of excercises NOT supported since support could be as low as 43.9%.

17. C1, L2, S17 Broadcasting Standards Poll Can it be claimed that: “More young people agree than disagree that there is too much sex, violence and bad language on TV” ? Dru Rose

18. C1, L2, S18 Difference in Poll %s Consider this scenario: MoE = 4% sample % who agree could be somewhere between 46% and 54% A likely new sample Difference in new sample poll %s = 8perct. pts = 2 × MoE A difference of more than 2 × MoE would be needed to disprove a claim of 50% agree 50% 54%46% Dru Rose

19. C1, L2, S19 Can it be claimed that more young people agree than disagree? Broadcasting Standards Poll (1) Sample Size Poll MoE MoE difference Difference 95% CI difference Meaning Judgement n = 600 2 x 4.1 = 8.2 perc. pts 51-44 = 7 perc. pts [ -1.2 perc pts., 15.2 perc. pts.] More young people may disagree than agree by up to 1.2 perc.pts and more young people may agree than disagree by up to 15.2 perc. pts Claim Not Supported 7 -1.2 15.2 Dru Rose

20. C1, L2, S20 MoE for difference = 8.6% (half CI) MoE Males MoE Females Rule of thumb for MoE difference = 1.5 x Av MoE = 1.5 x 6.3 =9% We can show that this works about 95% of the time Dru Rose

21. C1, L2, S21 Broadcasting Standards Poll (2) Can it be claimed that young women were more likely to agree than young men ? MoE women MoE me n Av MoE MoE difference 1.5 x 5.75 = 8.6% 95% CI differenc e[ 3.4 perc pts., 20.6 perc. pts. ] Difference meaning The % of Young women who agreed was somewhere between 3.4 and 20.6 perc. pts more than the % of young men Judgement Claim is supported 12 3.4 20.6 =57-45 = 12 perc. pts Dru Rose

22. Why teach AS3.12 ? Statistical Literacy is an essential life-skill to function effectively in the information age (Wallman, 1993; Gal, 2002) Broadens students’ horizons, taking statistical understanding beyond the classroom into the real world (a motivational aspect for students in the trial) Accessible to less academic students External standard Only pre-requisite is AS2.9 (possibly just 1.10) Links to other standards students may be taking (formal inference AS3.10, experiments AS3.11, bi-variate data AS 3.9 ) Dru Rose